I took a little time to look deeper at the idea of making a ukulele. Okay, sure, I have a uke already. A cheap Rogue with friction pegs, veneer top, and horrid intonation. I've been meaning to upgrade to a concert scale anyhow (slightly larger fret and string spacing but the same tuning). But I've also had a certain desire to try an electric instrument.
You can buy an electric uke. Most of them are electric-acoustic which is NOT the same thing. Of the steel strings, there are only a few options and most of the decent ones are expensive. What I want is something with the curves and shiny paint of a Strat or Tele, that plays like a uke, and when someone asks where I got it, I can tell them I made it. Or at least assembled the kit.
So I did some research. I could build a cigar-box uke without too much trouble. One downside to that is would probably be less playable than my Rogue; cheap materials and simple construction often leads to less-than-lovely tolerances, and for musical instruments tolerances matter. The other downside is that there's no point in having a second cheap uke. I want an upgrade.
Once you go steel-string, though, even with a solid-body, the mechanics become much more difficult. It is the same problem I had with the "Fury Gun" I built last year; in that case, it was five pounds of good Krups steel on 30" long barrels and I needed proper machined parts to keep it from falling apart under it's own weight.
And then add the problem of it being, well, a ukulele. I'm not going to be happy with string or fret spacing from an electric guitar (even if the tuning worked out, which it doesn't), or even an electric mandolin (for which you can find fairly inexpensive kits.) This was going to be a uke, dammit. Re-entrant tuning and all (unlike a guitar, the lowest pitched string is in the middle, not on the bottom).
So this means I need bridge, nut, and tuners that can handle steel strings. That's a bit of cost already. There's a company that makes a good bridge for a steel-string uke for about fifty bucks. A set of tuning machines will of course cost 20-40 dollars themselves. And you still need ferrules and so forth.
The tension of those steel strings is too much to trust a glued wood neck to. It needs reinforcement, preferably a double-action truss bar (so it can be adjusted to flatten the curve of the neck to within the close tolerances needed to make a properly set-up instrument). And no-one, of course, makes a uke neck with a truss bar. So that's either hand-carve one from twenty bucks of hardwood, or slot a pre-made neck -- as little as another twenty bucks for the pine neck of a cheap Grizzly kit, or a decent mahogany one for 35 to fifty dollars. Plus the truss rod of course!
And that doesn't necessarily cover the frets, which might require some time with fret wire. I am not a masochist, though; if I have to make my own fingerboard, I'll buy one pre-slotted (and pre-cambered).
A guitar pick-up has the wrong spacing and too many strings. You could hand-wind your own. Or you could get a decent four-string pick-up from Almuse for about fifty bucks. And add another twenty-thirty bucks for the basic electronics, and the cheapest set of parts that makes a decent electric uke comes out to at least two hundred bucks.
A temptation appears at this point; to go the other way and accept the challenge of making the cheapest possible electric uke. Scrap and salvage wood. Threaded steel rod for a truss rod. Actual wires for fret wires. But there are two big problems with this scheme. One is that time and money graph against each other. if you want to do it cheap, it will take longer. Perhaps much, much longer -- when you are talking about things like making your own tuners from scratch. The other is that cheap and substitute materials are too likely to end up with, again, a uke that is nearly unplayable. And more than any other goal, I want a decent instrument I can continue to learn and grow on.
So. As another alternative, could Frankenstein a Grizzly soprano kit ($22) and a Saga electric mandolin kit ($116) and make an instrument. At the end of it, though, you'd have a mandolin bridge -- not a solid-body guitar or uke style -- lousy electronics, and a soprano fretboard. And there's no guarantee you can hack a decent Les Paul teardrop out of the pre-carved mandolin body, or re-purpose the Saga truss rod into a Grizzly neck of an entirely different shape.
So it pretty much looks like you need to go the route of purchasing Moongazer bridges and Almuse pickups and Grover tuning machines from Stew-Mac, rent some shop time to fit a truss rod and carve a body from a nice chunk of hardwood, and spend a few bucks on top of that for epoxy paints and chrome miscellaneous hardware like strap pegs -- oh, yes, and shape a nice pick guard.
So the total cost in parts and tools is very likely to exceed $300. The time commit is not THAT bad, not with pre-slotted fingerboard and carved neck and pre-shaped bone nut and so forth. But all in all does not seem an appropriate project to start at this time.